package algorithm.algorithmsFourthEdition.RedBlackBST;

import java.util.NoSuchElementException;

/**
 * 算法第4版的红黑树代码
 * @param <Key>
 * @param <Value>
 */
public class RedBlackBST<Key extends Comparable<Key>, Value> {

    private static final boolean RED = true;
    private static final boolean BLACK = false;
    private Node root;

    // root of the BST // BST helper node data type
    private class Node {

        private Key key;
        private Value val;
        private Node left, right;
        private boolean color;
        private int N;    // node个数

        public Node(Key key, Value val, int N, boolean color) {
            this.key = key;
            this.val = val;
            this.N = N;
            this.color = color;
        }
    }

    public RedBlackBST() {

    }

    public int size() {
        return size(root);
    }

    private int size(Node node) {
        if (node == null) {
            return 0;
        } else {
            return node.N;
        }
    }

    private boolean isRed(Node x) {
        if (x == null) {
            return false;
        }

        return x.color == RED;
    }

    public boolean isEmpty() {
        return root == null;
    }

    public Value get(Key key) {
        if (key == null) {
            throw new NullPointerException("argument to get() is null");
        }

        return get(root, key);
    }

    // value associated with the given key in subtree rooted at x; null if no such key
    private Value get(Node x, Key key) {
        while (x != null) {
            int cmp = key.compareTo(x.key);
            if (cmp < 0) {
                x = x.left;
            } else if (cmp > 0) {
                x = x.right;
            } else {
                return x.val;
            }
        }
        return null;
    }


    public boolean contains(Key key) {
        return get(key) != null;
    }

    Node rotateLeft(Node h) {
        Node x = h.right;
        h.right = x.left;
        x.left = h;

        x.color = h.color;
        h.color = RED;
        x.N = h.N;
        h.N = 1 + size(h.left) + size(h.right);

        return x;
    }

    Node rotateRight(Node h) {
        Node x = h.left;
        h.left = x.right;
        x.right = h;

        x.color = h.color;
        h.color = RED;
        x.N = h.N;
        h.N = 1 + size(h.left) + size(h.right);

        return x;
    }

    private void flipColors(Node h) {
        h.color = RED;
        h.left.color = BLACK;
        h.right.color = BLACK;
    }

    public void put(Key key, Value val) {
        root = put(root, key, val);
        root.color = BLACK;
    }

    private Node put(Node h, Key key, Value val) {
        if (h == null) {
            return new Node(key, val, 1, RED);
        }
        int cmp = key.compareTo(h.key);
        if (cmp < 0) {
            h.left = put(h.left, key, val);
        } else if (cmp > 0) {
            h.right = put(h.right, key, val);
        } else {
            h.val = val;
        }

        if (isRed(h.right) && !isRed(h.left)) {
            h = rotateLeft(h);
        }
        if (isRed(h.left) && isRed(h.left.left)) {
            h = rotateRight(h);
        }
        if (isRed(h.left) && isRed(h.right)) {
            flipColors(h);
        }

        h.N = 1 + size(h.left) + size(h.right);

        return h;
    }

    public void deleteMin() {
        if (isEmpty()) {
            throw new NoSuchElementException("BST underflow");
        }
        // if both children of root are black, set root to red
        if (!isRed(root.left) && !isRed(root.right)) {
            root.color = RED;
        }
        root = deleteMin(root);
        if (!isEmpty()) {
            root.color = BLACK; // assert check();
        }
    }

    private Node deleteMin(Node h) {
        if (h.left == null) {
            return null;
        }

        if (!isRed(h.left) && !isRed(h.left.left)) {
            h = moveRedLeft(h);
        }

        h.left = deleteMin(h.left);
        return balance(h);
    }

    public void deleteMax() {
        if (isEmpty()) {
            throw new NoSuchElementException("BST underflow");
        }
        // if both children of root are black, set root to red
        if (!isRed(root.left) && !isRed(root.right)) {
            root.color = RED;
        }
        root = deleteMax(root);
        if (!isEmpty()) {
            root.color = BLACK;
        }
        // assert check();
    }

    // delete the key-value pair with the maximum key rooted at h
    private Node deleteMax(Node h) {
        if (isRed(h.left)) {
            h = rotateRight(h);
        }

        if (h.right == null) {
            return null;
        }

        if (!isRed(h.right) && !isRed(h.right.left)) {
            h = moveRedRight(h);
        }

        h.right = deleteMax(h.right);

        return balance(h);
    }

    public void delete(Key key) {
        if (key == null) {
            throw new NullPointerException("argument to delete() is null");
        }

        if (!contains(key)) {
            return;
        }
        // if both children of root are black, set root to red if (!isRed(root.left) && !isRed(root.right)) root.color = RED;
        root = delete(root, key);
        if (!isEmpty()) {
            root.color = BLACK;
        }
        // assert check();
    }

    // delete the key-value pair with the given key rooted at h
    private Node delete(Node h, Key key) {
        // assert get(h, key) != null;
        if (key.compareTo(h.key) < 0) {
            if (!isRed(h.left) && !isRed(h.left.left)) {
                h = moveRedLeft(h);
            }

            h.left = delete(h.left, key);
        } else {
            if (isRed(h.left)) {
                h = rotateRight(h);
            }
            if (key.compareTo(h.key) == 0 && (h.right == null)) {
                return null;
            }
            if (!isRed(h.right) && !isRed(h.right.left)) {
                h = moveRedRight(h);
            }
            if (key.compareTo(h.key) == 0) {
                Node x = min(h.right);
                h.key = x.key;
                h.val = x.val;
                // h.val = get(h.right, min(h.right).key);
                // h.key = min(h.right).key;
                h.right = deleteMin(h.right);
            } else {
                h.right = delete(h.right, key);
            }
        }
        return balance(h);
    }


    // Assuming that h is red and both h.left and h.left.left are black, make h.left or one of its children red.
    private Node moveRedLeft(Node h) {
        // assert (h != null);
        // assert isRed(h) && !isRed(h.left) && !isRed(h.left.left);
        flipColors(h);
        if (isRed(h.right.left)) {
            h.right = rotateRight(h.right);
            h = rotateLeft(h);
            flipColors(h);
        }
        return h;
    }

    // Assuming that h is red and both h.right and h.right.left are black, make h.right or one of its children red.
    private Node moveRedRight(Node h) {
        // assert (h != null);
        // assert isRed(h) && !isRed(h.right) && !isRed(h.right.left);
        flipColors(h);
        if (isRed(h.left.left)) {
            h = rotateRight(h);
            flipColors(h);
        }
        return h;
    }

    // restore red-black tree invariant
    private Node balance(Node h) {
        // assert (h != null);
        if (isRed(h.right)) {
            h = rotateLeft(h);
        }

        if (isRed(h.left) && isRed(h.left.left)) {
            h = rotateRight(h);
        }

        if (isRed(h.left) && isRed(h.right)) {
            flipColors(h);
        }

        h.N = size(h.left) + size(h.right) + 1;
        return h;
    }

    public int height() {
        return height(root);
    }

    private int height(Node x) {
        if (x == null) {
            return -1;
        }

        return 1 + Math.max(height(x.left), height(x.right));
    }

    public Key min() {
        if (isEmpty()) {
            throw new NoSuchElementException("called min() with empty symbol table");
        }

        return min(root).key;
    }

    // the smallest key in subtree rooted at x; null if no such key
    private Node min(Node x) {
        // assert x != null;
        if (x.left == null) {
            return x;
        } else {
            return min(x.left);
        }
    }

    public Key max() {
        if (isEmpty()) {
            throw new NoSuchElementException("called max() with empty symbol table");
        }

        return max(root).key;
    }

    // the largest key in the subtree rooted at x; null if no such key
    private Node max(Node x) {
        // assert x != null;
        if (x.right == null) {
            return x;
        } else {
            return max(x.right);
        }
    }

    public Key floor(Key key) {
        if (key == null) {
            throw new NullPointerException("argument to floor() is null");
        }

        if (isEmpty()) {
            throw new NoSuchElementException("called floor() with empty symbol table");
        }

        Node x = floor(root, key);
        if (x == null) {
            return null;
        } else {
            return x.key;
        }
    }

    // the largest key in the subtree rooted at x less than or equal to the given key
    private Node floor(Node x, Key key) {
        if (x == null) {
            return null;
        }

        int cmp = key.compareTo(x.key);
        if (cmp == 0) {
            return x;
        }

        if (cmp < 0) {
            return floor(x.left, key);
        }

        Node t = floor(x.right, key);
        if (t != null) {
            return t;
        } else {
            return x;
        }
    }

    public Key ceiling(Key key) {
        if (key == null) {
            throw new NullPointerException("argument to ceiling() is null");
        }

        if (isEmpty()) {
            throw new NoSuchElementException("called ceiling() with empty symbol table");
        }

        Node x = ceiling(root, key);
        if (x == null) {
            return null;
        } else {
            return x.key;
        }
    }

    // the smallest key in the subtree rooted at x greater than or equal to the given key
    private Node ceiling(Node x, Key key) {
        if (x == null) {
            return null;
        }
        int cmp = key.compareTo(x.key);
        if (cmp == 0) {
            return x;
        }
        if (cmp > 0) {
            return ceiling(x.right, key);
        }
        Node t = ceiling(x.left, key);
        if (t != null) {
            return t;
        } else {
            return x;
        }
    }

    public Key select(int k) {
        if (k < 0 || k >= size()) {
            throw new IllegalArgumentException();
        }

        Node x = select(root, k);
        return x.key;
    }

    // the key of rank k in the subtree rooted at x
    private Node select(Node x, int k) {
        // assert x != null;
        // assert k >= 0 && k < size(x);
        int t = size(x.left);
        if (t > k) {
            return select(x.left, k);
        } else if (t < k) {
            return select(x.right, k - t - 1);
        } else {
            return x;
        }
    }

    public int rank(Key key) {
        if (key == null) {
            throw new NullPointerException("argument to rank() is null");
        }

        return rank(key, root);
    }

    // number of keys less than key in the subtree rooted at x
    private int rank(Key key, Node x) {
        if (x == null) {
            return 0;
        }

        int cmp = key.compareTo(x.key);
        if (cmp < 0) {
            return rank(key, x.left);
        } else if (cmp > 0) {
            return 1 + size(x.left) + rank(key, x.right);
        } else {
            return size(x.left);
        }
    }

    public Iterable<Key> keys() {
        if (isEmpty()) {
            return new Queue<Key>();
        }

        return keys(min(), max());
    }

    public Iterable<Key> keys(Key lo, Key hi) {
        if (lo == null) {
            throw new NullPointerException("first argument to keys() is null");
        }

        if (hi == null) {
            throw new NullPointerException("second argument to keys() is null");
        }

        Queue<Key> queue = new Queue<Key>();
        // if (isEmpty() || lo.compareTo(hi) > 0) return queue;
        keys(root, queue, lo, hi);
        return queue;
    }

    // add the keys between lo and hi in the subtree rooted at x // to the queue
    private void keys(Node x, Queue<Key> queue, Key lo, Key hi) {
        if (x == null) {
            return;
        }
        int cmplo = lo.compareTo(x.key);
        int cmphi = hi.compareTo(x.key);
        if (cmplo < 0) {
            keys(x.left, queue, lo, hi);
        }
        if (cmplo <= 0 && cmphi >= 0) {
            queue.enqueue(x.key);
        }
        if (cmphi > 0) {
            keys(x.right, queue, lo, hi);
        }
    }

    public int size(Key lo, Key hi) {
        if (lo == null) {
            throw new NullPointerException("first argument to size() is null");
        }

        if (hi == null) {
            throw new NullPointerException("second argument to size() is null");
        }

        if (lo.compareTo(hi) > 0) {
            return 0;
        }

        if (contains(hi)) {
            return rank(hi) - rank(lo) + 1;
        } else {
            return rank(hi) - rank(lo);
        }
    }

    @SuppressWarnings("unused")
    private boolean check() {
        if (!isBST()) {
            System.out.println("Not in symmetric order");
        }

        if (!isSizeConsistent()) {
            System.out.println("Subtree counts not consistent");
        }

        if (!isRankConsistent()) {
            System.out.println("Ranks not consistent");
        }

        if (!is23()) {
            System.out.println("Not a 2-3 tree");
        }

        if (!isBalanced()) {
            System.out.println("Not balanced");
        }

        return isBST() && isSizeConsistent() && isRankConsistent() && is23() && isBalanced();
    }

    // does this binary tree satisfy symmetric order? // Note: this test also ensures that data structure is a binary tree since order is strict
    private boolean isBST() {
        return isBST(root, null, null);
    }

    // is the tree rooted at x a BST with all keys strictly between min and max // (if min or max is null, treat as empty constraint) // Credit: Bob Dondero's elegant solution
    private boolean isBST(Node x, Key min, Key max) {
        if (x == null) {
            return true;
        }
        if (min != null && x.key.compareTo(min) <= 0) {
            return false;
        }
        if (max != null && x.key.compareTo(max) >= 0) {
            return false;
        }
        return isBST(x.left, min, x.key) && isBST(x.right, x.key, max);
    }

    // are the size fields correct?
    private boolean isSizeConsistent() {
        return isSizeConsistent(root);
    }

    private boolean isSizeConsistent(Node x) {
        if (x == null) {
            return true;
        }
        if (x.N != size(x.left) + size(x.right) + 1) {
            return false;
        }
        return isSizeConsistent(x.left) && isSizeConsistent(x.right);
    }

    // check that ranks are consistent
    private boolean isRankConsistent() {
        for (int i = 0; i < size(); i++) {
            if (i != rank(select(i))) {
                return false;
            }
        }

        for (Key key : keys()) {
            if (key.compareTo(select(rank(key))) != 0) {
                return false;
            }
        }
        return true;
    }

    // Does the tree have no red right links, and at most one (left)
    // red links in a row on any path?
    private boolean is23() {
        return is23(root);
    }

    private boolean is23(Node x) {
        if (x == null) {
            return true;
        }

        if (isRed(x.right)) {
            return false;
        }

        if (x != root && isRed(x) && isRed(x.left)) {
            return false;
        }

        return is23(x.left) && is23(x.right);
    }

    // do all paths from root to leaf have same number of black edges?
    private boolean isBalanced() {
        int black = 0;
        // number of black links on path from root to min
        Node x = root;
        while (x != null) {
            if (!isRed(x)) {
                black++;
            }
            x = x.left;
        }
        return isBalanced(root, black);
    }

    // does every path from the root to a leaf have the given number of black links?
    private boolean isBalanced(Node x, int black) {
        if (x == null) {
            return black == 0;
        }
        if (!isRed(x)) {
            black--;
        }
        return isBalanced(x.left, black) && isBalanced(x.right, black);
    }

}

